. Question 1o v t > dy t Solve the separable differential equation . it 21: + I: Use the following initial condition: gm) 2 4. Write answer as a formula in the variable t. v \f0 Question 12 v ( > 8 (HS pts '0 6553 A roasted turkey is taken from an cwen when its temperature has reached 185 Fahrenheit and is placed on a table in a room where the temperature is ?5 Fahrenheit. Give answers accurate to at least 2 decimal places. (a) If the temperature of the turkey is 143 Fahrenheit alter half an hour, what is its temperature after 45 minutes? (b) When will the turkey:r coal to l Fahrenheit? 0 Question 13 v ( > 8 0:5 pts '0 55535 5 Let yj} represent your bank account balance, in dollars, alter .tyears. Suppose you start with $40000 in the account. Each year me account earns 4% interest, and you deposit $8000 into me account. This can be modeled with the differential equation: y 004 +3000 {it _ ' 1" yrn) =40000 Solve this differential equation for yft) 0 Question 14 v ( > 8 m5 pts '0 65535 S- A manufacturer estimates diet she can sell a maximum of 1m thousand cell phones in a city. By advertising heavily, her total sales grew at a rate proportional to the distance below this upper limit. If she enters a new market, and after 2 months her total sales are 64 thousand phones, find a formula for the total sales (in thousands) {months after entering the market, and use this to estimate the total sales at the end of the rst year. Total sales at end of the rst year: :] thousand phones Give your answer to at least 1 decimal place 0 Question 15 v ( > E ors pts '0 65535 A bacteria culture starts with 36D bacteria and grows at a rate proportional to its size. After 3 hours there will be 1080 bacteria. (a) Express the population P after t hours as a function of t. Be sure to keep at least 4 signicant gures on the growth rate. Pm= (b) What will be the population after 4 hours? bacteria (c) How long will it take for the population to reach 241i]? Give your answer accurate to at least 2 decimal places. hours 0 Question 15 v E are pts '0 65535 E 99 G) Details Suppose you have just poured a cup of freshly brewed coffee with temperature QCv' in a room where the temperature is 20 (3'. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature di'erence between the object and its surroundings. Therefore, the temperature of the coffee, T[t}, satises the differential equation dT where TM 2 2|] is the room temperature, and k is some constant. Suppose it is known that the coffee cools at a rate of 1"(3f per minute when its temperature is TWO. A. What is the limiting value of the temperature of the coffee? as... w = :1 B. What is the limiting value of the rate of cooling? J'.I:I1 GIT Hts-Cl C. Find the constant k in the differential equation. D. Use Euler's method with step size I; = 1 minutes to estimate the temperature of the coffee after 5 minutes. me = :l